# RepLoRA: Reparameterizing Low-Rank Adaptation via the Perspective of Mixture of Experts

arXiv: https://arxiv.org/abs/2502.03044 · HTML: https://mlsanity.com/paper/2502.03044/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Mixture of LoRA experts, one of 12 directions in Mixture-of-experts.
- Builds on 40 of its 58 references that are in the map.
- First posted on arXiv 5 Feb 2025.

## Placed in

- Mixture-of-experts / [Mixture of LoRA experts](https://mlsanity.com/moe/mixture-of-lora-experts/)

## Builds on (most cited first, 30 of 40)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Making the V in VQA Matter: Elevating the Role of Image Understanding in Visual Question Answering](https://mlsanity.com/paper/1612.00837/) (2016)
- [Visual Prompt Tuning](https://mlsanity.com/paper/2203.12119/) (2022)
- [The "something something" video database for learning and evaluating visual common sense](https://mlsanity.com/paper/1706.04261/) (2017)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [Towards Automatic Learning of Procedures from Web Instructional Videos](https://mlsanity.com/paper/1703.09788/) (2017)
- [Is ChatGPT a General-Purpose Natural Language Processing Task Solver?](https://mlsanity.com/paper/2302.06476/) (2023)
- [TVQA: Localized, Compositional Video Question Answering](https://mlsanity.com/paper/1809.01696/) (2018)
- [A Corpus for Reasoning About Natural Language Grounded in Photographs](https://mlsanity.com/paper/1811.00491/) (2018)
- [HERO: Hierarchical Encoder for Video+Language Omni-representation Pre-training](https://mlsanity.com/paper/2005.00200/) (2020)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [VL-Adapter: Parameter-Efficient Transfer Learning for Vision-and-Language Tasks](https://mlsanity.com/paper/2112.06825/) (2021)
- [Learning Factored Representations in a Deep Mixture of Experts](https://mlsanity.com/paper/1312.4314/) (2013)
- [From Sparse to Soft Mixtures of Experts](https://mlsanity.com/paper/2308.00951/) (2023)
- [TVR: A Large-Scale Dataset for Video-Subtitle Moment Retrieval](https://mlsanity.com/paper/2001.09099/) (2020)
- [Controlling Text-to-Image Diffusion by Orthogonal Finetuning](https://mlsanity.com/paper/2306.07280/) (2023)
- [FuseMoE: Mixture-of-Experts Transformers for Fleximodal Fusion](https://mlsanity.com/paper/2402.03226/) (2024)
- [Residual Prompt Tuning: Improving Prompt Tuning with Residual Reparameterization](https://mlsanity.com/paper/2305.03937/) (2023)
- [Mixture of Experts Meets Prompt-Based Continual Learning](https://mlsanity.com/paper/2405.14124/) (2024)

## Built on by (most cited first, 6 of 6)

- [Promoting Ensemble Diversity with Interactive Bayesian Distributional Robustness for Fine-tuning Foundation Models](https://mlsanity.com/paper/2506.07247/) (2025)
- [One-Prompt Strikes Back: Sparse Mixture of Experts for Prompt-based Continual Learning](https://mlsanity.com/paper/2509.24483/) (2025)
- [DoRAN: Stabilizing Weight-Decomposed Low-Rank Adaptation via Noise Injection and Auxiliary Networks](https://mlsanity.com/paper/2510.04331/) (2025)
- [Hypernetwork-Driven Low-Rank Adaptation Across Attention Heads](https://mlsanity.com/paper/2510.04295/) (2025)
- [Rethinking Multinomial Logistic Mixture of Experts with Sigmoid Gating Function](https://mlsanity.com/paper/2602.01466/) (2026)
- [Queryable LoRA: Instruction-Regularized Routing Over Shared Low-Rank Update Atoms](https://mlsanity.com/paper/2605.08423/) (2026)

## Abstract (arXiv)

Low-rank Adaptation (LoRA) has emerged as a powerful method for fine-tuning large-scale foundation models. Despite its popularity, the theoretical understanding of LoRA has remained limited. This paper presents a theoretical analysis of LoRA by examining its connection to the Mixture of Experts models. Under this framework, we show that simple reparameterizations of the LoRA matrices can notably accelerate the low-rank matrix estimation process. In particular, we prove that reparameterization can reduce the data needed to achieve a desired estimation error from an exponential to a polynomial scale. Motivated by this insight, we propose Reparameterized Low-Rank Adaptation (RepLoRA), which incorporates lightweight MLPs to reparameterize the LoRA matrices. Extensive experiments across multiple domains demonstrate that RepLoRA consistently outperforms vanilla LoRA. Notably, with limited data, RepLoRA surpasses LoRA by a margin of up to 40.0% and achieves LoRA's performance with only 30.0% of the training data, highlighting both the theoretical and empirical robustness of our PEFT method.